This paper considers methods for the feedback control of thermoacoustic oscillations. Two distinct approaches to the problem are considered. The first is robust model-based control, which involves two stages: finding a model of the system, and designing a controller based on that model. The focus is on using model reduction techniques to find a low-order, balanced model of the Rijke tube which, despite having few degrees of freedom, is useful for feedback control design purposes. The second approach uses adaptive (or self-tuning) control, which does not require a model of the system, but instead requires that it meets some general properties. The focus here is on reducing how much must be known a priori about the plant. Specifically, an adaptive controller is considered which does not require knowledge of the sign of the plant's high-frequency gain, and this is done by employing a Nussbaum gain. The controllers are successfully applied in experiments on a Rijke tube. Both controllers completely eliminate oscillations, and in both cases stability is maintained following a large change in operating conditions.